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Question
The points (7, – 6), (2, k) and (h, 18) are the vertices of triangle. If (1, 5) are the coordinates of centroid, find the value of h and k
Solution
Let (7, – 6) ≡ (x1, y1), (2, k) ≡ (x2, y2), (h, 18) ≡ (x3, y3) be the three vertices of the triangle.
(1, 5) are coordinates of centroid.
∴ By Centroid formula,
1 = `(x_1 + x_2 + x_3)/3`
∴ 1 = `(7 + 2 + "h")/3`
∴ 3 = 9 + h
∴ h = – 6
5 = `(y_1 + y_2 + y_3)/3`
∴ 5 = `(-6 + "k" + 18)/3`
∴ 15 = 12 + k
∴ k = 3
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The coordinates of the vertices of a triangle ABC are A (–7, 6), B(2, –2) and C(8, 5). Find coordinates of its centroid.
Solution: Suppose A(x1, y1) and B(x2, y2) and C(x3, y3)
x1 = –7, y1 = 6 and x2 = 2, y2 = –2 and x3 = 8, y3 = 5
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ABC = `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`
= `(square/3, square/3)`
∴ Coordinates of the centroid of a triangle ABC = `(3/3, square)`
∴ Coordinates of the centroid of a triangle ABC = `(1 , square)`
Find the centroid of the ΔABC whose vertices are A(–2, 0), B(7, –3) and C(6, 2).
